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Mar 6, 2014 at 16:26 comment added guacho Is your $f=P_y*g$ for some $g$? Maybe the result is not true for every $p$. Is the result true for $p=2$, i.e., given $g\in H^1(\mathbb{R})$, is $P_y*g\in L^2(\mathbb{R}\times\mathbb{R}^+)$?
Mar 2, 2014 at 15:53 history edited Alexandre Eremenko CC BY-SA 3.0
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Mar 2, 2014 at 4:42 history edited Alexandre Eremenko CC BY-SA 3.0
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Mar 2, 2014 at 4:36 history answered Alexandre Eremenko CC BY-SA 3.0